Even though the Federal Reserve voted unanimously to raise a key interest rate last month, some policymakers viewed their decision as a "close call" given on-going concerns about stubbornly low inflation.

Going forward, officials believed economic conditions will likely justify "only gradual increases" in its benchmark rate, minutes of the Fed's meeting released Wednesday showed.

The Fed boosted the rate by a quarter point to a new range of 0.25 percent to 0.5 percent in December. It had been at a record low near zero for the past seven years.

Policymakers said they were "reasonably confident" that inflation would eventually move to the Fed's 2 percent target. At the time, they expressed significant concerns that it may stay weak, especially because of further declines in oil prices recently.

Many private economists believe the central bank will raise rates three or four times in 2016 with some expecting one quarter-point move at every other meeting. The Fed meets eight times a year.

However, the minutes did not make any reference to a specific number of rate hikes. Instead, they used the word "gradual" to underscore their view that rate hikes are likely to occur slowly.

"Participants saw several reasons why a gradual removal of policy accommodation would likely be appropriate," the minutes said.

Among the reasons cited: A slow pace for rate hikes would keep interest rates mild enough to further boost the labor market. The gains would then exert upward pressure on inflation, which has been stuck below the Fed's goal of 2 percent for more than three years.

Gradual rate hikes would also give the Fed time to assess how the economy was adjusting to the rate increase. A "cautious approach" to rate increases would also minimize any risks that the Fed would encounter in the event of an unforeseen economic shock.

In a CNBC interview broadcast Wednesday, Fed Vice Chairman Stanley Fischer said that the possibility of four interest rate increases this year are "numbers in the ballpark" of what the central bank will likely do. But he said, "we don't know enough now to know how many there will be."

Fischer described market expectations of just two rate hikes this year "too low."

The Fed next meets on Jan. 26-27.